Ploughed upland drains are straight prismatic channels of low aspect ratio. The drains are either uniformly or compositely roughened. In compositely roughened drains the bed and side-walls are differentially roughened although each roughness type is homogeneous. Upland catchments, containing extensive ploughed drainage networks, are particularly prone to flash flooding and increased sediment yield. However, the basic hydraulic data necessary to route flow through the drainage network and improve the engineering design of stable drainage channels are currently unavailable. A logarithmic flow resistance equation is developed for low aspect ratio channels, where the effective Nikuradse equivalent grain size is known. Testing against field data indicates that the relationship successfully predicts the resistance to uniform flow through upland drains. The performance of eight composite roughness formulae to predict the mean velocity in differentially roughened channels is compared. The composite roughness equations involve dividing the cross-sectional flow area into a number of sub-areas. The different methods of cross-sectional area division are considered and their effect on mean velocity prediction examined. Preferences are indicated concerning composite roughness equations which predict the mean velocity in channels of simple cross-sectional shape. Empirical equations are derived to determine the mean bed and side-wall shear stresses in straight symmetrical trapezoidal and rectangular open channels, with uniform or composite roughness. The model proposed is appropriate for stable sub-critical and super-critical flows. The equations are based on data collected from laboratory channels and should be cautiously applied to larger scale channels. Using the mean shear stress model, a design procedure is proposed to improve drainage channel stability.